Attaining exponential convergence for the flux error with second- and fourth-order accurate finite-difference equations. Part 3. Application to electrochemical systems comprising second-order chemical reactions

The present paper presents, numerical computations for flow, heat transfer and chemical reactions in an axisymmetric inert porous burner. The porous media re-radiate the heat absorbed from the gaseous combustion products by convection and conduction. In the present work, the porous burner species mass fraction source terms are computed from an ‘extended’ reaction mechanism, controlled by chemical kinetics of elementary reactions. The porous burner has mingled zones of porous/nonporous reacting flow, i.e. the porosity is not uniform over the entire domain. Therefore, it has to be included inside the partial derivatives of the transport governing equations. Finite-difference equations are obtained by formal integration over control volumes surrounding each grid node. Up-wind differencing is used to insure that the influence coefficients are always positive to reflect the real effect of neighboring nodes on a typical central node. Finite-difference equations are solved, iteratively, for U, V, p’ (pressure correction), enthalpy and species mass fractions, utilizing a fine grid of (80×60) nodes. The eighty grid nodes in the axial direction are needed to resolve the detailed structure of the thin reaction zone inside the porous media. The radial grid is extended inside the annular solid wall of the porous burner, to compute the wall temperature. The porous burner uses a premixed CH4-air mixture, while its radiating characteristics are computed numerically, using a four-flux radiation model. Sixteen species are included, namely CH4, CH3, CH2, CH, CH2O, CHO, CO, CO2, O2, O, OH, H2, H, H2O, H2O, H2O2, involving 49 chemical reaction equations. It was found that 1000 iterations are sufficient for complete conversion of the computed results with errors less than 0.1%. The computed temperature profiles of the gas and the solid show that, heat is conducted from downstream to the upstream of the reaction zone. Most stable species, such as H2O, CO2, H2, keep increasing inside the reaction zone staying appreciable in the combustion products. However, unstable products, such as HO2, H2O2 and CH3, first increase in the preheating region of the reaction zone, they are then consumed fast in the post-reaction zone of the porous burner. Therefore, it appears that their important function is only to help the chemical reactions continue to their inevitable completion of the more stable combustion products.

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Second-order finite-difference equations with constant coefficients in the rational function field

USSR Computational Mathematics and Mathematical Physics ◽

10.1016/0041-5553(77)90135-5 ◽

1977 ◽

Vol 17 (3) ◽

pp. 24-29 ◽

Cited By ~ 1

Author(s):

S.A. Abramov

Keyword(s):

Finite Difference ◽

Rational Function ◽

Difference Equations ◽

Function Field ◽

Second Order ◽

Rational Function Field ◽

Finite Difference Equations ◽

Constant Coefficients

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